Hey guys,
We answered the question differently than the answers and would like you to verify it if possible:
answer: since L in P and p=np, then L in NP as well.
So we have the 1st term for NPC.
by the cook-levin sentence, for every L' in NP there's a polynomial reduction to SAT that it is in NPC.
Therefor, there's a reduction from L to any L' in NP.
what do you think?
thanks =x

First, how did you conclude that if "for every L' in NP there's a polynomial reduction to SAT", then "there's a reduction from L to any L' " ?
Second, even if you proved that there's a reduction from L to any L' in NP, this is not the definition of NPC.
You need to prove the other way around - L is NPC if there's a reduction from any L' in NP to L.